Thin Films of Soft Matter
July 18, 2005 — July 22, 2005
Coordinators:
- Serafim Kalliadasis (Imperial College London, London, Great Britain)
- Uwe Thiele (Loughborough University, Loughborough, Great Britain)
Thin film flows of soft matter (either simple Newtonian liquids or polymeric and other complex materials) are encountered in a wide variety of natural phenomena and technological applications. The involved scales range from the nanometer level as for dewetting thin polymer films to the meter scale as for lava flows.
In the vast majority of cases, thin film and jet flows are bounded by either free surfaces which separate the films from the surrounding phases or by a free surface and a solid substrate. From the scientific point of view such free-surface flows are extremely important. They are part of the general class of free-boundary problems which hold a strategic position both in pure and applied sciences. The occurrence of free-boundaries and interfaces, i.e. material or geometric frontiers between regimes with different physical properties not “a priori” prescribed, arises in an enormous number of inherently nonlinear problems in fluid and solid mechanics, combustion, financial mathematics, materials science and glaciology.
Within the context of fluid mechanics in particular, the study of free-surface thin film and jet flows encounters in addition to the presence of a free boundary, several challenging aspects and complexities. Not surprisingly therefore, such flows have been an active topic of fundamental research for several decades. In this course we present a detailed overview of the main advances in the area of free surface flows in confined geometries, i.e. thin films and jets. We start with the basic equations and interfacial boundary conditions and derive model equations for the evolution of the free surface. The models include long-wave expansions and equations of the boundary-layer type. The course will cover linear stability analysis, weakly and strongly nonlinear analysis including construction of stationary periodic and solitary wave and similarity solutions. The focus will be on the dynamics of falling films, fingering instabilities of advancing and receding fronts, coating over topography, dewetting on chemically homogeneous and heterogeneous substrates, thermocapillary instabilities and jet break-up. We shall also discuss in detail a variety of very recent experimental developments and whenever possible we shall illustrate the strong link between theory and experiments. Such experiments include spreading drops and bubbles, imbibition, singularity formation at interfaces and experimental characterization of thin films using atomic force microscopy, ellipsometry and contact angle measurements and analysis of patterns using Minkowski functionals.
The course is addressed to beginning researchers, graduate students and post-doctoral fellows in all areas of engineering, science and applied mathematics wishing to master the fundamentals of free-surface thin film and jet flows. It is also geared towards all researchers with a general interest in interfacial fluid mechanics and more generally the mechanics of active dissipative-dispersive nonlinear media.